How do I get a Drizzle Politoed?

Solution 1:

Poliwag does appear in hordes in the Pokemon Village, but Poliwhirl with better stats and chances at a hidden ability can be found in Friend Safaris. If you want a Drizzle Politoed, you'll have to find a Water-type Friend Safari that contains Poliwhirl and catch one whose ability is Swift Swim.

Once you have said Poliwhirl, evolving it to Politoed should have it end up with the Drizzle ability.

Solution 2:

You can get Poliwhirl from the Friend Safari if you have a friend who is Water type who has beaten the Elite Four. This will have a good chance of having the hidden ability if you are online at the same time as your friend; a Poliwhirl with Swift Swim will evolve into a Politoed with Drizzle.

Source: Serebii